MinT - Best Known (51, 111, s)-Nets in Base 5

Best Known (51, 111, s)-Nets in Base 5

(51, 111, 82)-Net over F₅ — Constructive and digital

Digital (51, 111, 82)-net over F₅, using

t-expansion [i] based on digital (48, 111, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(51, 111, 104)-Net over F₅ — Digital

Digital (51, 111, 104)-net over F₅, using

net from sequence [i] based on digital (51, 103)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 51 and N(F) ≥ 104, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(51, 111, 1139)-Net in Base 5 — Upper bound on s

There is no (51, 111, 1140)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 391440 347227 228054 559615 366893 646157 549749 155876 973051 660165 280974 096840 598465 > 5¹¹¹ [i]